Test 3

For the description of these tests see paper

L.Beilina

ENERGY ESTIMATES AND NUMERICAL VERIFICATION OF THE STABILIZED DOMAIN DECOMPOSITION FINITE ELEMENT/FINITE DIFFERENCE APPROACH FOR THE MAXWELL'S SYSTEM IN TIME DOMAIN

Accepted for publication in CEJM, 2012.

Pdf file of preprint

In computational tests  presented here we solve the Maxwell’s system  in time T = [0, 20] in two dimensions with the known smooth solution

E1(x, y, t) = (t^2/2.0) *cos(πx) * sin(πy),

E2(x, y, t) = (−t^2/2.0)*sin(πx) * cos(πy).

In FEM domain coefficient μ = 1 and ε  is defined as a function

ε(x) = . 1 + 3*(sin( π/3 x))^2 · (sin(π/3)y)^2, 0 ≤ x ≤ 3, and −3 ≤ y ≤ 0;

1, at all other points  of FEM domain,

see Figure 1-a) for this function. In FDM our coefficients are ε = μ = 1

Figure 1-a)

Test 4 of paper: computed E_2h component in time of the electric field E_h=(E_1h, E_2h) in the

whole FEM/FDM computational domain.

Test 4 of paper: computed E_1h component in time of the electric field E_h=(E_1h, E_2h) in the

whole FEM/FDM computational domain. We observe small reflections from inhomogeneous FEM domain as soon wave approaches this domain.

Test 4 of paper: computed modulus of the  electrical field |E_h | = sqrt(E_1h*E_1h +  E_2h*E_2h) in time in the

whole FEM/FDM computational domain. Here, computed E_1h and E_2h components are presented in the two videos above.

Test 4 of paper: computed E_2h component in time of the electric field E_h=(E_1h, E_2h) in the

   inner FEM  domain.

Test 4 of paper: computed E_1h component in time of the electric field E_h=(E_1h, E_2h) in the

  inner FEM domain.

Test 4 of paper: computed modulus of the  electrical field |E_h | = sqrt(E_1h*E_1h +  E_2h*E_2h) in time in the

  inner FEM  domain.

Test 4 of paper: computed E_2h component in time of the electric field E_h=(E_1h, E_2h) in the

  outer  FDM domain.

Test 4 of paper: computed modulus of the  electrical field |E_h | = sqrt(E_1h*E_1h +  E_2h*E_2h) in time in the

  outer FDM  domain.